If the propellant is on board with the object, then it's mass increases with the object and tends to infinity; it should be sufficient to provide the infinite energy source. But, back to your earlier point, I believe there is no proof of this ever happening.
I think you need to re-read some basic physics here.
infinite energy would exceed the energy of the known universe, but I think we've accelerated electrons up to at least 99.99997 percent the speed of light.
Alspector et al., Phys. Rev. Lett. 36, pg 837 (1976).
A comparison of neutrino and muon velocities, at Fermilab.
Kalbfleisch et al., Physics Review Letters 43, pg 1361 (1979).
A comparison of muon, neutrino, and antineutrino velocities over a range of energies, at Fermilab.
Guiragosian et al., Phys. Rev. Lett. 34 no. 6 (1975), pg 335.
Relative velocity measurements of 15 GeV electrons and gammas. No significant difference was observed within ~2 parts in 107. See also Brown et al.
G.L. Greene et al.,“Test of special relativity by a determination of the Lorentz limiting velocity: Does E=mc2?” Physical Review D 44 (1991) R2216.
An analysis combining the results of several experiments gives the result that the Lorentz limiting velocity must be equal to the speed of light to within 12 parts per million.
Stodolsky, “The Speed of Light and the Speed of Neutrinos”, Phys. Lett. B201 no. 3 (1988), pg 353.
A comparison of neutrino and photon speeds from supernova SN1987A puts a limit of about 1 part in 108 on their speed difference.
I think you need to re-read some basic physics here.